Set 2: Y=5, Y=3X, Y=1X
Set 3: Y=2X+3, Y=2X-5, Y=0.5+2
Set 4:Y=2X, Y=2÷X, Y=X+5
A1. Which two equations in the set are have graphs that are similar?
In set 1,the equations Y=3X+2 and Y=3X-4 are similar. In set 2, Y=1X and Y=3X are similar. In set 3, Y=2X+3 and Y=2X-5, and in set 4, Y=X+5 and Y=2X. A2. In what ways are the two graphs similar?
In set 1, the two graphs are similar because they are both straight parallel lines. In set 2, Y=1X and Y=3X, they both have positive slopes. In set 3, the graphs are straight, positively sloped and parallel lines. In set 4 they are straight and positively sloped lines.
A3. In what ways are the equations for the two graphs similar?
In set 1, both equations have 3X in them. In set 2, the equations both have Y=X. In set 3, both have Y=2X, and in set 4, Y=2X and Y=2÷X are similar because they both have Y=2.
B1. Which equation in the set has a graph that is different from the other graphs?
In set 1, the graph for Y=X² is different. In set 2, Y=5 is different. In set 3, Y=0.5X+2, and in set 4, Y=2÷X is different.
B2. In what way is the graph different from the other graphs?
In set 1, Y=X² is different because it has a curved graph. In set 2, Y=5 is horizontal and is also constant. In set 3, Y=0.5X-2 is different because it is a very flat positive slope. In set 4, Y=2÷X is different because it is a pair of symmetrical curves in quadrant 1 and 3. As the -Y becomes very large (in quadrant 3) the -X becomes closer to 0. If +Y becomes very large (in quadrant 1), then +X becomes closer to 0. the same thing happens with Y values when +X or -X become very large.
B3. In what way is the equation different from the other equations?
In set 1, Y=X² is the only equation with the ² sign. In set 2, Y=5 is the only equation without an X. In set 3, Y=0.5X+2 does'nt have a 2X, and in set 4, Y=X+5 does'nt have a 2.
Follow up
Use the equation Y=2X to answer the following:
1A. If X=2, Y=4
1B. If X = 2/3, then Y=1 and 1/3
1C. If X= 3.25, then Y=6.5
1D. Table showing pairs of numbers fitting equation Y=2X
Y
0
2
4
6
8
10
12
X
0
1
2
3
4
5
6
2. Table showing pairs of numbers fitting equation Y=2X+ 3
Y
3
5
7
9
11
13
15
X
0
1
2
3
4
5
6
3. How are the two tables above similar?
The tables for problems 1D and 2 are similar because they are both basicaly the same thing, except for the fact that the table for problem 2, Y is always 3 higher than the Y in table for problem 1D for a given value of X.
Naasik Syed
Math 7B
10-3-09
Experimenting with a graphing calculator
Problem 5.1 Using a Graphing Calculator
Sets
Set 1: Y=3X-4, Y=X², Y=3X+2Set 2: Y=5, Y=3X, Y=1X
Set 3: Y=2X+3, Y=2X-5, Y=0.5+2
Set 4:Y=2X, Y=2÷X, Y=X+5
A1. Which two equations in the set are have graphs that are similar?
In set 1,the equations Y=3X+2 and Y=3X-4 are similar. In set 2, Y=1X and Y=3X are similar. In set 3, Y=2X+3 and Y=2X-5, and in set 4, Y=X+5 and Y=2X.A2. In what ways are the two graphs similar?
In set 1, the two graphs are similar because they are both straight parallel lines. In set 2, Y=1X and Y=3X, they both have positive slopes. In set 3, the graphs are straight, positively sloped and parallel lines. In set 4 they are straight and positively sloped lines.
A3. In what ways are the equations for the two graphs similar?
In set 1, both equations have 3X in them. In set 2, the equations both have Y=X. In set 3, both have Y=2X, and in set 4, Y=2X and Y=2÷X are similar because they both have Y=2.
B1. Which equation in the set has a graph that is different from the other graphs?
In set 1, the graph for Y=X² is different. In set 2, Y=5 is different. In set 3, Y=0.5X+2, and in set 4, Y=2÷X is different.
B2. In what way is the graph different from the other graphs?
In set 1, Y=X² is different because it has a curved graph. In set 2, Y=5 is horizontal and is also constant. In set 3, Y=0.5X-2 is different because it is a very flat positive slope. In set 4, Y=2÷X is different because it is a pair of symmetrical curves in quadrant 1 and 3. As the -Y becomes very large (in quadrant 3) the -X becomes closer to 0. If +Y becomes very large (in quadrant 1), then +X becomes closer to 0. the same thing happens with Y values when +X or -X become very large.
B3. In what way is the equation different from the other equations?
In set 1, Y=X² is the only equation with the ² sign. In set 2, Y=5 is the only equation without an X. In set 3, Y=0.5X+2 does'nt have a 2X, and in set 4, Y=X+5 does'nt have a 2.
Follow up
Use the equation Y=2X to answer the following:
1A. If X=2, Y=4
1B. If X = 2/3, then Y=1 and 1/3
1C. If X= 3.25,
then Y=6.5
1D. Table showing pairs of numbers fitting equation Y=2X
2. Table showing pairs of numbers fitting equation Y=2X+ 3
3. How are the two tables above similar?
The tables for problems 1D and 2 are similar because they are both basicaly the same thing, except for the fact that the table for problem 2, Y is always 3 higher than the Y in table for problem 1D for a given value of X.